Vieira rolled back the years against Aston Villa in a dominant display as City's holding midfielder and Mancini believes the 33-year-old, who arrived at Eastlands in January looking short of fitness, can still earn a place in France's World Cup squad.
Wednesday night's match at home to Spurs could prove to be a decider for fourth spot in the Premier League, though both sides have a final match to play after that.
Mancini believes a victory over Spurs would be extra special for City's ex-Gunner Vieira, Kolo Toure and Emmanuel Adebayor.
"Tottenham beat Arsenal three weeks ago and so I hope that Patrick, Kolo and Emmanuel can beat Tottenham in their own 'derby'," said Mancini.
"I'm happy for Patrick, he was fantastic against Aston Villa and he has great experience.
"He had a lot of problems when he arrived here, he's a tall player and needs to play and work every day.
"Now I think he has time to make the World Cup, and I hope he does.
"I asked him to play in a certain position, don't run forward, just stay there and think, and he played very well."
If Vieira was man of the match against Villa, Adam Johnson came a close second for the a first-half performance that saw him create City's two first goals.
He earned a penalty for the first, smashed down the middle by Carlos Tevez, and set up Adebayor for a neat finish for the second, leading Mancini to predict an important future for him at the club and for England.
Craig Bellamy rounded off the victory as Villa, who had had a storming run in April, ran out of legs despite taking an early lead through John Carew.
Villa boss Martin O'Neill has been the subject of some speculation over his future but insisted he is committed to the club, and will take inspiration from the example set by Sir Alex Ferguson.
He said: "If you are asking if I have the desire to go back again? Of course, that's what makes sport so great. You have to have that desire to go back again. "If you take a leaf out of someone at Manchester United, you take great delight in winning championships and then putting it aside and the season starts and you go again next year.
"I enjoy the job but I have told the players if they can get a real career out of football don't think about management, take a cushy coaching job, particularly with Alex Ferguson at the helm.
"If I could have come back in another life I would be reserve team coach under Alex Ferguson and you are kind of safe."
O'Neill will meet Villa chairman Randy Lerner next week to discuss the future, with summer transfers top of the list.
He added: "The chairman is coming over for a few days, hopefully he will take in last game of the season.
"I will sit down with him and discuss all aspects about the season. If it's like he was telling me a couple of weeks ago - he's been immensely proud of the team.
"Obviously we have to try and get stronger and we would need to do that, which is easier said than done. The next question will be about the size of the squad."